Mon. Not. R. Astron. Soc. 427, 688–702 (2012) doi:10.1111/j.1365-2966.2012.21900.x Hubble Space Telescope Hα imaging of star-forming galaxies at z 1–1.5: evolution in the size and luminosity of giant H II regions R. C. Livermore, 1T. Jones, 2 J. Richard, 1,3 R. G. Bower, 1 R. S. Ellis, 2 A. M. Swinbank, 1 J. R. Rigby, 4 Ian Smail, 1 S. Arribas, 5 J. Rodriguez-Zaurin, 6 L. Colina, 5 H. Ebeling 7 and R. A. Crain 8 1 Institute for Computational Cosmology, Durham University, South Road, Durham DH1 3LE 2 Astronomy Department, California Institute of Technology, MC 249-17, Pasadena, CA 91125, USA 3 CRAL Observatoire de Lyon, 9 Avenue Charles Andr´ e, 69561 Saint-Genis-Laval, France 4 NASA Goddard Space Flight Center, Code 665, Greenbelt, MD 20771, USA 5 Centro de Astrobiologia, Departamento de Astrof´ ısica, CSIC-INTA, Ctra. de Ajalvir km. 4, 28850 Torrej´ on de Ardoz, Madrid, Spain 6 Instituto de Astrof´ ısica de Canarias (IAC), C/Via L´ actea s/n, E38205, La Laguna, Tenerife, Spain 7 Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA 8 Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, the Netherlands Accepted 2012 August 8. Received 2012 July 13; in original form 2012 May 23 ABSTRACT We present Hubble Space Telescope/Wide Field Camera 3 narrow-band imaging of the Hα emission in a sample of eight gravitationally lensed galaxies at z = 1–1.5. The magnification caused by the foreground clusters enables us to obtain a median source plane spatial resolution of 360 pc, as well as providing magnifications in flux ranging from ∼10× to ∼50×. This enables us to identify resolved star-forming H II regions at this epoch and therefore study their Hα luminosity distributions for comparisons with equivalent samples at z ∼ 2 and in the local Universe. We find evolution in the both luminosity and surface brightness of H II regions with redshift. The distribution of clump properties can be quantified with an H II region luminosity function, which can be fit by a power law with an exponential break at some cut-off, and we find that the cut-off evolves with redshift. We therefore conclude that ‘clumpy’ galaxies are seen at high redshift because of the evolution of the cut-off mass; the galaxies themselves follow similar scaling relations to those at z = 0, but their H II regions are larger and brighter and thus appear as clumps which dominate the morphology of the galaxy. A simple theoretical argument based on gas collapsing on scales of the Jeans mass in a marginally unstable disc shows that the clumpy morphologies of high-z galaxies are driven by the competing effects of higher gas fractions causing perturbations on larger scales, partially compensated by higher epicyclic frequencies which stabilize the disc. Key words: gravitational lensing: strong – galaxies: high-redshift – galaxies: star formation. 1 INTRODUCTION Observations of star-forming galaxies at high-z have shown that a significant fraction of the population has turbulent, clumpy, rotating discs with clump masses of ∼10 8−9 M , a factor of ∼100× the typi- cal giant molecular cloud (GMC) locally (e.g. Cowie, Hu & Songaila 1995; Elmegreen et al. 2004, 2009; Elmegreen & Elmegreen 2005; F¨ orster Schreiber et al. 2009). The clumps are thought to form from gravitational instabilities in gas-rich discs (Elmegreen et al. 2007, 2009; Genzel et al. 2008; Bournaud et al. 2010). Some recent numerical simulations have suggested that the ma- jority of massive, high-z galaxies accrete their gas via ‘cold flows’, E-mail: [email protected]in which the gas is accreted smoothly along filaments. These cold flows are less disruptive than a major merger, and hence offer a route to maintain marginally stable discs (Toomre parameter Q ∼ 1) with- out disrupting the structure and dynamics. Cold-flow accretion is expected to be a dominant mode of mass assembly above z 1, and thus accounts for the ubiquity of large clumps at high redshift (e.g. Bournaud & Elmegreen 2009; Dekel, Sari & Ceverino 2009; Bournaud et al. 2011). In this picture, the clumps are considered to be transient features, forming in marginally unstable discs at high-z and fed by smooth ac- cretion of gas on to the galaxy. Clumpy galaxies therefore represent a phase in the evolution of present-day spiral discs. There is a need to test the internal physical properties of the in- terstellar medium (ISM) observationally to determine whether the clumps are scaled-up analogues of local H II regions or represent a C 2012 The Authors Monthly Notices of the Royal Astronomical Society C 2012 RAS https://ntrs.nasa.gov/search.jsp?R=20140010551 2020-06-14T01:23:22+00:00Z
Transcript
Mon. Not. R. Astron. Soc. 427, 688–702 (2012) doi:10.1111/j.1365-2966.2012.21900.x
Hubble Space Telescope Hα imaging of star-forming galaxies at z � 1–1.5:evolution in the size and luminosity of giant H II regions
R. C. Livermore,1� T. Jones,2 J. Richard,1,3 R. G. Bower,1 R. S. Ellis,2
A. M. Swinbank,1 J. R. Rigby,4 Ian Smail,1 S. Arribas,5 J. Rodriguez-Zaurin,6
L. Colina,5 H. Ebeling7 and R. A. Crain81Institute for Computational Cosmology, Durham University, South Road, Durham DH1 3LE2Astronomy Department, California Institute of Technology, MC 249-17, Pasadena, CA 91125, USA3CRAL Observatoire de Lyon, 9 Avenue Charles Andre, 69561 Saint-Genis-Laval, France4NASA Goddard Space Flight Center, Code 665, Greenbelt, MD 20771, USA5Centro de Astrobiologia, Departamento de Astrofısica, CSIC-INTA, Ctra. de Ajalvir km. 4, 28850 Torrejon de Ardoz, Madrid, Spain6Instituto de Astrofısica de Canarias (IAC), C/Via Lactea s/n, E38205, La Laguna, Tenerife, Spain7Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA8Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, the Netherlands
Accepted 2012 August 8. Received 2012 July 13; in original form 2012 May 23
ABSTRACTWe present Hubble Space Telescope/Wide Field Camera 3 narrow-band imaging of the Hα
emission in a sample of eight gravitationally lensed galaxies at z = 1–1.5. The magnificationcaused by the foreground clusters enables us to obtain a median source plane spatial resolutionof 360 pc, as well as providing magnifications in flux ranging from ∼10× to ∼50×. Thisenables us to identify resolved star-forming H II regions at this epoch and therefore study theirHα luminosity distributions for comparisons with equivalent samples at z ∼ 2 and in the localUniverse. We find evolution in the both luminosity and surface brightness of H II regions withredshift. The distribution of clump properties can be quantified with an H II region luminosityfunction, which can be fit by a power law with an exponential break at some cut-off, and wefind that the cut-off evolves with redshift. We therefore conclude that ‘clumpy’ galaxies areseen at high redshift because of the evolution of the cut-off mass; the galaxies themselvesfollow similar scaling relations to those at z = 0, but their H II regions are larger and brighterand thus appear as clumps which dominate the morphology of the galaxy. A simple theoreticalargument based on gas collapsing on scales of the Jeans mass in a marginally unstable discshows that the clumpy morphologies of high-z galaxies are driven by the competing effects ofhigher gas fractions causing perturbations on larger scales, partially compensated by higherepicyclic frequencies which stabilize the disc.
Observations of star-forming galaxies at high-z have shown that asignificant fraction of the population has turbulent, clumpy, rotatingdiscswith clumpmasses of∼108−9 M�, a factor of∼100× the typi-cal giantmolecular cloud (GMC) locally (e.g. Cowie,Hu&Songaila1995; Elmegreen et al. 2004, 2009; Elmegreen & Elmegreen 2005;Forster Schreiber et al. 2009). The clumps are thought to form fromgravitational instabilities in gas-rich discs (Elmegreen et al. 2007,2009; Genzel et al. 2008; Bournaud et al. 2010).Some recent numerical simulations have suggested that the ma-
jority of massive, high-z galaxies accrete their gas via ‘cold flows’,
in which the gas is accreted smoothly along filaments. These coldflows are less disruptive than amajor merger, and hence offer a routeto maintain marginally stable discs (Toomre parameterQ ∼ 1) with-out disrupting the structure and dynamics. Cold-flow accretion isexpected to be a dominant mode of mass assembly above z � 1,and thus accounts for the ubiquity of large clumps at high redshift(e.g. Bournaud & Elmegreen 2009; Dekel, Sari & Ceverino 2009;Bournaud et al. 2011).In this picture, the clumps are considered to be transient features,
forming inmarginally unstable discs at high-z and fed by smooth ac-cretion of gas on to the galaxy. Clumpy galaxies therefore representa phase in the evolution of present-day spiral discs.There is a need to test the internal physical properties of the in-
terstellar medium (ISM) observationally to determine whether theclumps are scaled-up analogues of local H II regions or represent a
Evolution in the properties of giant H II regions 689
different ‘mode’ of star formation, and whether they can explain thestrong evolution of star formation rate (SFR) density with redshift.However, sufficient spatial resolution is required to resolve the ISMon the scales of star-forming regions. Even with the use of adaptiveoptics, spatially resolved studies of high-redshift galaxies to datehave been limited to a resolution of ∼1.5 kpc (e.g. Genzel et al.2006; Forster Schreiber et al. 2009); using the Hubble Space Tele-scope (HST), only the largest starburst complexes can be resolved,on scales of ∼1 kpc (Elmegreen et al. 2007). On these scales, itis possible to probe the dynamics of galaxies on large scales, andGenzel et al. (2011) found evidence that Q < 1 in the regions ofgalaxies where clumps are found, lending observational support tothe theory that the clumps form from internal gravitational insta-bilities. In order to study the clumps in detail, we need to resolvehigh-redshift discs on the scales of individual star-forming regions;in the local universe, this is ∼100 pc.The required spatial resolution can currently only be achieved
by exploiting gravitational lensing. By targeting galaxies that liebehind foreground cluster lenses, it is possible to benefit from lin-ear magnification factors (along one direction) of up to 50× (e.g.Swinbank et al. 2007, 2009; Jones et al. 2010), and to isolate H II
regions of order ∼100 pc out to z ∼ 5 (Swinbank et al. 2009). Re-gionswere foundwith star formation surface densities�SFR ∼100×higher than those found locally (Swinbank et al. 2009; Jones et al.2010). These regions of dense star formation are comparable tothe most intensely star-forming interacting systems in the localUniverse (Bastian et al. 2006), yet appear to be ubiquitous in non-interacting galaxies at high redshift.It is not known what drives these regions of intense star forma-
tion at high-z, although Jones et al. (2010) suggest a combination ofhigher gas density, increased star formation efficiency and shorterstar formation time-scales. In addition, their data give the appear-ance of a bimodal distribution of H II region surface brightnesses,although there is no known physical process that might drive this.In order to understand this result further, we require a sample atintermediate redshift (z ∼ 1–1.5) with which we can probe the evo-lution of star formation density with redshift at higher sensitivity sothat regions comparable to those at z = 0 are detectable.Previous work on high-z clumps has made use of integral
field units such as Keck/OH-Suppessing Infrared Integral FieldSpectrograph (OSIRIS; Jones et al. 2010; Wisnioski et al. 2012),
Gemini/Near-Infrared Integral Field Spectrometer (NIFS;Swinbank et al. 2009) and Very Large Telescope(VLT)/Spectrograph for Integral Field Observations in the NearInfrared (SINFONI; Forster Schreiber et al. 2009). These allowdetailed mapping of the nebular emission lines, but at lowersensitivity than is achievable with imaging. An alternative meansof identifying star-forming regions with high sensitivity is to takeimaging through narrow-band filters. The Wide Field Camera 3(WFC3) on the HST presents an opportunity to study the starformation in galaxies at z ∼ 1 and ∼1.5, as there are narrow-bandfilters available which correspond to the wavelength of the Hα
emission line at these redshifts. Combining the sensitivity and highspatial resolution of HST/WFC3 with the magnification affordedby gravitational lensing by foreground clusters, we can map theinternal star formation distribution and so identify the frequencyand properties of giant H II regions.In this paper, we therefore study the star formation morphologies
of eight galaxies at z ∼ 1–1.5. We present the sample in Section 2,present the properties of the galaxies and their star-forming clumpsin Section 3, discuss the implications in Section 4 and present ourconclusions in Section 5. Throughout, we adopt a � cold darkmatter (�CDM) cosmology with H0 = 70 km s−1 Mpc−1, �� =0.7 and �m = 0.3. SFRs are calculated from Hα luminosity LHα
using the prescription of Kennicutt (1998a) adjusted to a Chabrier(2003) initial mass function (IMF).
2 SA M P L E A N D O B S E RVAT I O N S
Our sample comprises eight lensed galaxies, each with spectro-scopically confirmed redshifts in the range 1 < z < 1.5 such thatthe Hα emission line falls within the high-transmission region ofthe narrow-band filters on WFC3. The associated cluster lenses aremassive systems from the X-ray selected Brightest Cluster Sam-ple (BCS) and Massive Cluster Survey (MACS) samples (Ebelinget al. 1998, 2007, 2010; Ebeling, Edge & Henry 2001) with well-constrained mass models (see references in Table 1), so that theeffects of lensing can be accounted for.The positions and properties of the sample are given in Table 1.
We observed each target in the narrow-band filter covering Hα fora typical exposure time of 6 ks (2 orbits), using a 3- or 4-pointlinear dithering pattern of ±5 arcsec in both directions to improve
Table 1. Properties of the redshift-selected sample. Lensing magnifies the image by a factor μx at a position angle (PA), with a transverse magnification μy.The total magnification factor μ is calculated from the amplification of Hα flux, and the resolution given is the highest achievable along the most magnifieddirection, calculated from the FWHM of a star under the same lensing transformation as that applied to the galaxy, as described in the text. All observationswere obtained under Program 12197 (Cycle 18, PI: Richard) unless otherwise stated.
Target cluster Arc position z Hα flux Magnification Resolution Broad-band Narrow-band LensRA Dec. (intrinsic) μx × μy (PA) μ (pc) filter filter model
aProgram 12065-9; bProgram 11678; cProgram 11591; dEbeling et al. (2010); eEbeling et al. (in preparation); fEbeling et al. (2007).References: [1] Richard et al. (2010); [2] Pello et al. (1991); [3] Richard et al. (in preparation); [4] Richard et al. (2007); [5] Smith et al. (2009); [6] Sand et al.(2005).
the detection and removal of cosmic ray hits and bad pixels. Atthe same time, three of the targets (MACS J0947, MACS J0159and MACS J1133), which did not have WFC3 data in the archive,were observed in the corresponding broad-band filter using thesame sequence of observations as their corresponding narrow-banddata, for a total of 3 ks (1 orbit). The narrow-band data and newbroad-band observations were obtained in Cycle 18 under Program12197 (PI: Richard), with the exception of Abell 2390, for whichthe broad-band and narrow-band data were taken in Cycle 17 underProgram 11678 (PI: Rigby). The remaining broad-band data wereobtained under Cycle 17 Program 11591 (PI: Kneib) or Cycle 18Program 12065-9 (PI: Postman) as indicated in the notes to Table 1.All of the WFC3 data were reduced using the MULTIDRIZZLE soft-
ware (Koekemoer et al. 2002) under PyRAF to perform a cosmicray rejection, sky subtraction and drizzling on to an output pixelscale of 0.05 arcsec. The narrow-band and broad-band images of thesame cluster were aligned using the location of ∼20 bright stars. Anarrow-band excess image was constructed by direct pixel-to-pixelsubtraction between the narrow-band and broad-band images, in-cluding an arbitrary scaling factor. We calibrated this scaling factorby checking that all bright cluster members, which are featurelesselliptical galaxies with no emission lines in the respective filters,became consistent with the background in the excess image. ForAbell 773 and Abell 68, the broad-band images available in thearchive did not directly overlap the Hα emission line, so an esti-mate of the broad-band continuumwas made by linear interpolationbetween the adjacent F110W and F160W filters.The flux calibration of each imagewas verified using TwoMicron
All Sky Survey (2MASS) stars in the fields, and in all cases wasfound to agree to within 15 per cent, which is sufficient precisionfor our purposes.Colour HST images of the clusters are shown in Fig. 1, with
the critical lines at the redshift of the target arc overlaid. We use thetransformation between image and source plane mapping from thebest-fitting cluster mass models (for details of the mass models,see references in Table 1) with LENSTOOL (Kneib 1993; Jullo et al.2007) to reconstruct the images in the source plane, and show thesein Fig. 2. In order to reconstruct the source plane morphology,LENSTOOL uses the mapping between the image and source planeson a cluster-by-cluster basis and ray traces the galaxy image. Thelensing effect is to stretch the galaxy image – in most cases alongone direction – and so the reconstruction cannot ‘create’ new H II
regions, but rather the lensing has acted to extend them. As surfacebrightness is conserved by lensing, we then apply this conservationto obtain the intrinsic source plane flux. The total magnification isthen simply the ratio of the image- to source plane flux. To obtainthe errors on the magnification, we use the family of best-fitting lensmodels which adequately describe the cluster potential, derived bysampling the posterior probability distribution of each parameterof the model (see Richard et al. 2010 for more details). For eachacceptable lens model, we reconstruct the arc and remeasure theamplification. We give the resulting magnification factors, μ, andassociated errors in Table 1.In cases where the target is multiply imaged, the images were
reconstructed separately and then adjusted for small differences inposition and orientation before being combined. For MACS J0159,which consists of five images, only the first three were used dueto the high magnification gradients in the fourth and fifth imagesresulting in high distortion in the source plane reconstructions. Inthe case of Abell 611, we use only the northernmost arc due to highdistortion by a foreground galaxy lying close to the line of sight ofthe southern arc.
We derive total magnification factors by comparing the total lu-minosities of the image- and source plane Hα excess images. Theintrinsic Hα luminosities are in the range 0.45–15 × 1041 erg s−1
corresponding to SFRs of 0.4–12M� yr−1. These are at the faintend of the Hα luminosity function (LF) for this redshift range (seeFig. 3), and probe fainter galaxies than the z ∼ 2 sample of Joneset al. (2010), which covers the range 2.5–32 × 1041 erg s−1, al-though the two samples overlap in luminosity. Because of theincreased sensitivity provided by the lensing magnification, bothof the lensed samples cover a lower range of intrinsic Hα lumi-nosities than the sample of Spectroscopic Imaging Survey in theNear-Infrared with SINFONI (SINS) galaxies studied by ForsterSchreiber et al. (2011b), which were selected to have bright Hα andlie in the range 28–43 × 1041 erg s−1, making them rare, intenselystar-forming galaxies. Thus, by harnessing gravitational lensing weare able to probe the more ‘normal’ star-forming population.Since gravitational lensing can preferentially shear one direction,
we estimate the effective source plane resolution by reconstructingthe image of a star from the field repositioned to lie at the centreof the target. The maximum linear resolution, derived from the fullwidth at half-maximum (FWHM) of the reconstructed star in thedirection of greatest magnification, is 68–615 pc with a median of360 pc, sufficient to resolve giant H II regions.
2.1 Comparison samples
In order to interpret our high-z data, we exploit the Hα narrow-band imaging from the Spitzer Infrared Nearby Galaxies Survey(SINGS; Kennicutt et al. 2003), which comprises Hα imaging of75 galaxies with corrected SFRs of up to 11M� yr−1. We use thepublicly available continuum-subtracted Hα narrow-band imagingand restrict the sample to those with Hα detections with signal-to-noise ratio of >5 that have no significant defects in the galaxyimages (determined by visual inspection). This restricts the SINGSsample to 41 galaxies with SFR > 4 × 10−4 M� yr−1.To ensure a fair comparison, we rebin the SINGS images so that
the resolution is comparable to the high-z data and then threshold tothe median surface brightness limit of the z ∼ 1–1.5 observations. Itis worth noting that thresholding the images in this manner excludes10–50 per cent of the total star formation. This should not affect thecomparison between samples which have the same surface bright-ness limit, but may serve as an indication of the fraction of starformation missed in high-z observations.To provide a comparison to local galaxies which are more ac-
tively star forming, we use the Visible Multi-Object Spectrograph(VIMOS) Hα imaging spectroscopy of Rodrıguez-Zaurın et al.(2011), which includes 38 luminous infrared galaxies (LIRGs) andultraluminous infrared galaxies (ULIRGs) at z < 0.13 with spatialresolution of 130–1.2 kpc and SFR � 25M� yr−1.We also compare the z ∼ 1–1.5 sample to the z ∼ 2 lensed arcs
of Jones et al. (2010), which were observed with Keck/OSIRIS. Inorder to provide a fair comparison, we have constructed narrow-band images by summing the OSIRIS cubes over 100Å either sideof the redshifted Hα emission line, matching the width of theWFC3narrow-band filters. The resulting images are then corrected forlensing using the same image-to-source plane mapping as Joneset al. (2010) in order to obtain the intrinsic galaxy properties.
2.2 Determination of galaxy properties
The total Hα luminosities of the galaxies in all samples are de-termined by summing all pixels in sky-subtracted images withsignal-to-noise ratio of >3. In the case of the SINGS galaxies,
Evolution in the properties of giant H II regions 691
Figure 1. HST/ACS andWFC3 three-colour images of the observed clusters with the critical line at the redshift of the target arc overlaid, showing the positionsof the target arcs. The arcs are contained within the white dashed boxes which denote the regions extracted in Fig. 2.
each image was checked by visual inspection and any foregroundsources and defects masked. The resulting luminosities were thencompared to the published values and found to agree to within∼20 per cent.
We convert Hα luminosity to SFR using the Kennicutt (1998a)prescription, corrected to a Chabrier (2003) IMF, which reducesthe SFR by a factor of 1.7×. As we do not have constraintson the dust extinction, we adopt an estimate of AHα = 1 in all
Figure 2. Hα excess images in the image plane (left) and reconstructed in the source plane (right). The image scales are in arcsec in the image plane and inkpc in the source plane. Identified clumps are indicated in the source plane images by black crosses, and the magenta ellipse shows the FWHM of the effectivesource plane PSF, as described in the text.
samples. This assumption is widely used in the literature althoughit is the subject of some disagreement. Garn et al. (2010) sug-gest a luminosity-dependent AHα is more appropriate; were we toadopt their relation, we would obtain AHα = 0.7–1.6 with a medianAHα = 1.15. However, we also note that recent work by Domınguezet al. (2012) suggests that galaxies with LHα � 4 × 1041 erg s−1
may be consistent with having AHα = 0, and that above this thresh-old extinction increases in a luminosity-dependent way. Had weadopted this correction instead, the SFRs of the majority of ourgalaxies would be reduced by a factor of 2.5×. The exceptionsare the three brightest z ∼ 2 galaxies, in which the SFRs would
increase by factors of 1.3–1.8×, and the z ∼ 1 galaxies Abell 68and Abell 773; the former would be a factor of 1.8× lower, whilethe latter would be unchanged. Qualitatively, there is no significantimpact on our results, as adopting either luminosity-dependent ex-tinction relation would serve to increase the evolution we observe inSection 3.2.2. For simplicity and reproducibility, we adopt AHα = 1throughout.We define the sizes of the galaxies as twice the half-light radius.
The half-light radius is determined using the continuum images tofind the shape (i.e. the centre and major to minor axis ratio of an el-lipse that best fits the galaxy), and then adjusting the semimajor axis
Evolution in the properties of giant H II regions 693
Figure 3. Intrinsic Hα luminosities of the high-z samples compared to Hα
LFs from High-z Emission Line Survey (HiZELS; Sobral et al. 2012). Alsoshown is the range of Hα luminosities of the Forster Schreiber et al. (2011b)sample from the SINS survey at z ∼ 2. The two lensed samples overlap inluminosity and are both at the faint end of the LF, with the median of the z ∼1–1.5 WFC3 sample lower than that of the z = 1.6− 2.6 OSIRIS sample bya factor of 6.6×, while the unlensed SINS galaxies cover a range of higherHα luminosities.
of the ellipse until it encompasses half of the total Hα luminositycalculated in the manner described above. The galaxy-averaged starformation surface density,�SFR, is defined from the total luminosityenclosed within two half-light radii per unit area.
3 R E S U LT S A N D A NA LY S I S
3.1 The spatial distribution of star formation
A common theme in the recent literature is that high-redshift galax-ies are ‘clumpier’ than galaxies in the local Universe. This conceptoriginates from the frequent appearance of ‘chain’ galaxies in thehigh-redshift universe (e.g. Cowie et al. 1995; Elmegreen et al.2004; Elmegreen & Elmegreen 2005). Even without looking at theproperties of individual star-forming regions, it is interesting tocompare the morphologies of the star-forming regions across thesamples.From visual inspection, it is clear that there are significant dif-
ferences between the samples. In particular, the surface brightnessdistributions of the galaxies show distinct differences in the differ-ent samples. In Fig. 4, we show the fraction of star formation inpixels above a given�SFR for the z ∼ 1–1.5 and z ∼ 2 samples, withthe interquartile range of the thresholded SINGS sample shown forcomparison.To allow for the differing surface brightness limits of the samples,
we only show star formation above a surface brightness of �SFR =0.001M� yr−1 kpc−2. This enables us to compare the star formationoccurring in bright regions in a consistent manner. From the peaks
– i.e. the points at which the lines tend to zero – we can see that thesamples are different, with the z ∼ 2 galaxies having peak surfacebrightnesses of around an order of magnitude higher than the lowerz samples. Similarly, the z ∼ 1–1.5 sample is systematically brighterthan the SINGS sample, with the exception of MACS J1133, whichis similar to the fainter z = 0 galaxies, MACS J0947which is similarto the median of the z = 0 sample, and Abell 773 which appearssimilar to the z ∼ 2 galaxies.As a statistical measure of the clumpiness of galaxies, we inves-
tigate using the Gini coefficient, G, which is used in economics tomeasure the inequality of wealth in a population (Gini 1912). It hasvalues from 0 to 1, where at the extremes G = 0 for a completelyuniform distribution, and G = 1 if there is only one non-zero value.Following Forster Schreiber et al. (2011a), we use it to quantify thedistribution of flux in an image, so a value close to one indicatesthat the profile has a single peak (in the case of G = 1, all of theflux would be in a single pixel), a galaxy with multiple clumpswould have a lowerG, and at the extreme, a galaxy with completelyuniform surface brightness would have G = 0.In the z ∼ 1–1.5 sample, we find a narrow range of 0.25 ≤ G ≤
0.39 with a median of G = 0.34. The z ∼ 2 sample is marginallyhigher, with 0.42 ≤ G ≤ 0.56 and a median of G = 0.43. Thez = 0 SINGS sample has a similar median G = 0.45 but a muchwider range of 0.05 ≤ G ≤ 0.82, and the low-z (U)LIRGs have0.38 ≤ G ≤ 0.85 with the highest median G = 0.70. On the basisof the Gini coefficient there are no clear differences between thesamples. Comparing theGini coefficientswith the visual appearanceof the galaxies, the lack of distinction reflects the fact that a lowGini coefficient may arise from either a smooth distribution ofstar formation or from star formation that is concentrated into alarge number of distinct clumps. Furthermore, we find no strongcorrelations between G and any of the properties of the galaxies.Clearly, to progress further we will have to compare the propertiesof individual clumps. In particular, we will show that the clumpLF provides a good means of distinguishing different galaxy starformation morphologies.
3.2 Properties of star-forming clumps
3.2.1 Definition of clumps
Studies of H II regions or star-forming clumps have used a varietyof methods to define and separate clumps from the backgroundemission of the galaxy. Usually an isophote is defined at 3σ abovethe background noise (e.g. Gonzalez Delgado & Perez 1997; Joneset al. 2010). However, this method is clearly dependent on the noiseproperties of the image, and thus is problematic when comparinglocal and high-redshift observations. In particular, as high-redshiftgalaxy images tend to have high relative noise levels and low dy-namic range, the choice of isophote tends to select only the bright-est regions in the galaxy, neglecting any lower surface brightnessclumps and underestimating their sizes.An alternative is the IRAF task DAOFIND as employed by Forster
Schreiber et al. (2011b), which is designed to locate point sourcesin images. However, we found that it did not perform well on oursample. This is likely to be because DAOFIND requires an expectedsize of features to look for. As the clumps of Forster Schreiberet al. (2011b) are largely unresolved, they were able to use the pointspread function (PSF) of their observations as the expected size. Asour clumps are resolved, the routine does not work reliably. For thispaper, we therefore use the 2D version of CLUMPFIND (Williams, deGeus&Blitz 1994), which usesmultiple isophotes to define clumps.
Figure 4. The fraction of star formation within each galaxy occurring above a given surface brightness, for the z ∼ 1–1.5 and z ∼ 2 samples. The shadedregion is the interquartile range of the SINGS z ∼ 0 sample. There are two galaxies, MACS J1133 and MACS J0947, from the z ∼ 1–1.5 sample with similarsurface brightnesses to the z = 0 sample, and the remainder are systematically brighter. The z ∼ 2 sample has significantly higher surface brightnesses. Hence,there is clear evolution in the surface brightnesses of galaxies with redshift.
We defined the contour levels with respect to the rms noise in theimage, starting at 3σ and increasing in 1σ intervals until the peakvalue of the image is reached. The data are first contoured at thehighest level to locate clumps, and the algorithm then works downin brightness through the contour levels. Any isolated contours aredefined as new clumps, while others extend existing clumps. Ifa contour surrounds one existing peak, they are allocated to thatclump, and any which enclose two or more are divided using a‘friends-of-friends’ algorithm. The advantages of this approach arethat it enables a consistent clump definition to be applied to multipledata sets, lower surface brightness clumps are not excluded and thereis no assumption made about the clump profile.The clumps identified by CLUMPFIND were all confirmed by vi-
sual inspection to remove any source not associated with the targetgalaxy, of particular importance in the case of the SINGS imageswhere foreground sources lie close to or overlap the target galax-ies. The area A of the clump is then obtained from the number ofpixels assigned to it, multiplied by the source plane pixel scale, andfrom this we define the effective radius r = √
A/π. We only acceptclumps where 2r is larger than the FWHM of the PSF, so all clumpsare resolved.
Because of the manner in which clumps are ‘grown’, their sizesreturned by CLUMPFIND tend to be larger than those obtained byother methods. As a comparison, we also fit a 2D elliptical Gaus-sian profile to each peak and measure the FWHM. A comparisonof the clump radii found by the two methods is shown in Fig. 5.The rms difference between the two radii is ∼100 pc, and on av-erage we find that CLUMPFIND outputs sizes 25 per cent higher thanthe FWHM. Wisnioski et al. (2012) note that sizes defined throughisophotes can be unreliable due to the level of ‘tuning’ requiredto select an appropriate isophote level in a given galaxy. This isless significant with CLUMPFIND because this tuning is not required;the use of multiple isophote levels in all galaxies allows the lev-els to be defined in a consistent way across a large sample. Wetherefore find much lower scatter between the isophotal sizes out-put by CLUMPFIND and the clump FWHM than they do in theirsample. Throughout this work, we use the CLUMPFIND size for allsamples, and give error bars that encompass the FWHM of theclumps.The sizes and Hα-derived SFRs of the z ∼ 1–1.5 clumps are given
in Table 2. We analyse these properties in comparison to the othersamples below.
Evolution in the properties of giant H II regions 695
Figure 5. Comparison of the clump size rclumpfind output by CLUMPFIND withthe size rFWHM obtained by taking the FWHM of a 2D Gaussian profile fit.On average, CLUMPFIND outputs sizes 25 per cent larger than the FWHM. Forconsistency, we adopt the isophotal size output by rclumpfind in all samples.
3.2.2 Clump properties
One way of quantifying the ‘clumpiness’ of a galaxy is to considerthe fraction of a galaxy’s total Hα luminosity contained withinclumps. We find medians of 31 per cent in SINGS, 36 per cent forthe z < 0.13 ULIRGs, 50 per cent for the z ∼ 1–1.5 sample and68 per cent for the z ∼ 2 sample. Thus, as expected, the higher zgalaxies are clumpier than their local counterparts.We now consider the properties of the clumps themselves, and
first compare the Hα-derived SFR to the clump radius, as shown inFig. 6. Locally, there is a well-defined relationship between theseproperties, as found by Kennicutt (1988) who found almost con-stant surface brightness in local H II regions, except in merging andinteracting systems (Bastian et al. 2006). The situation at high-z,though, appears different; Swinbank et al. (2009) and Jones et al.(2010) found clumps with SFRs of ∼100× higher at a given sizethan found locally, in systems with no evidence of interactions.Fig. 6 is an updated version of one presented in Jones et al.
(2010), where we have re-analysed the z ∼ 2 and SINGS galaxiesusing CLUMPFIND so that clumps are defined consistently across allsamples, and we have added the results from our new z ∼ 1–1.5data set and the z < 0.13 ULIRGs as well as the z = 1–2 resultsfrom SHiZELS (Swinbank et al. 2012) and WiggleZ (Wisnioskiet al. 2012). We show lines of median surface brightness in thesamples, and vertical offsets from these lines represent differencesin the surface density of star formation, �SFR, in the clumps. Wewill explore the relation of these offsets to global galaxy propertiesin Section 4.We note that the clumps we identify in the SINGS galaxies are
derived from images which have been degraded to comparable reso-lution to the high-z data, and we find the effect of this is to decreasethe surface brightness by a factor of ∼2×, as the size increasesmore than the luminosity. The points in Fig. 6 move along the vectorlabelled ‘A’. Defining clumps in the z = 0 sample in this way ensuresthe fairest possible comparison with the high-z data.Upon re-analysis using CLUMPFIND, we find some lower �SFR re-
gions in the Jones et al. (2010) sample, but they all remain separated
Table 2. Properties of clumps identified in the z ∼ 1–1.5 sample,determined as described in Section 3.2.1.
from the local relation by a factor of ∼100×. This confirmsthe large differences between the local and high-redshift popu-lation already noted by Swinbank et al. (2009) and Jones et al.(2010).Our new z ∼ 1–1.5 sample fits in between the SINGS and z ∼ 2
samples, with the exception of the two regions from the most
Figure 6. Hα SFR for extracted H II regions as a function of size, compared to the lensed z ∼ 2 sample of Jones et al. (2010), high-z unlensed samples fromSHiZELS (Swinbank et al. 2012) and WiggleZ (Wisnioski et al. 2012), low-z (U)LIRGs from Rodrıguez-Zaurın et al. (2011) and the z = 0 SINGS galaxies(Kennicutt et al. 2003). SFRs are calculated using the Kennicutt (1998a) prescription adjusted for a Chabrier IMF with a dust extinction AHα = 1 in all samples,and the error bars of the high-z lensed sources are dominated by the uncertainty in the lensing magnification. Dashed lines show the median surface brightnessesin the SINGS, z ∼ 1–1.5 and z ∼ 2 samples. The black dotted line indicates the sensitivity limit of the z ∼ 2 OSIRIS observations. The arrow indicates theeffect of degrading the image resolution, as discussed in the text. The four lowest surface brightness clumps in the z ∼ 1–1.5 sample come from one galaxy(MACS J1133), and the two brightest regions are from Abell 773, the most compact galaxy in the sample. The remaining galaxies have clumps with surfacebrightnesses in between those of the z = 0 and z ∼ 2 samples, similar to local (U)LIRGs.
compact source Abell 773, which have �SFR similar to the z ∼2 sample, and the four regions fromMACS1133, which are similarto z = 0 clumps. This indicates clear evolution in clump surfacebrightness, �SFR, with redshift.The surface brightness limit of the z ∼ 2 data means that we
cannot identify the low SFR clumps in that sample. We show adotted line representing the lower limit at whichwe define clumps inthe z ∼ 2 galaxies. It is likely that there are additional clumps whichlie below this limit and are undetected; however, such clumps makeonly a small contribution to the total SFR, as we shall discuss inSection 3.3.Selection effects have no impact on the lack of high surface
brightness regions in the lower redshift samples, however. The in-tense star-forming regions are clearlymore common in high-z galax-ies; they are found only in extreme systems such as the Antennaelocally, but exist in all five of the z ∼ 2 galaxies and one of the eightz ∼ 1–1.5 sample.As noted in Section 2, the z ∼ 2 galaxies have ‘normal’ SFRs
for their redshift, below the knee of the Hα LF. The offsets seen inthe figure emphasize the importance of analysing clumps in termsof their surface brightness. This is even more evident if the clumpsbelonging to a single galaxy are examined separately. Rather thanbeing distributed across the plot at random, individual galaxies form
a much tighter sequence with all the clumps sharing a commonsurface brightness, particularly in the low-redshift sample. Thus thespread in clump properties in Fig. 6 appears to be driven by globaldifferences in the galaxies.We therefore next compare the clump �SFR to the properties of
their host galaxies in Fig. 7. In the left-hand panel, we correlate theclump properties with the total SFR of the galaxy. For clarity, weplot the median clump�SFR in each individual galaxy, and the errorbars encompass the central 68 per cent of clumpswithin each galaxy(i.e. 1σ if they follow a Gaussian distribution). There is evidence forcorrelation between the clump �SFR and the galaxy Hα luminosity(which we assume to be proportional to the total SFR); we find aSpearman rank correlation coefficient ρ = 0.69, representing a 5.8σdeviation from the null hypothesis of no correlation. This suggeststhat the star formation in the high-z sample follows a similar trendto the local sample, and that the differences seen in Fig. 6 may arisefrom the higher total SFRs of the high-redshift galaxies.For the majority of the samples, an even stronger relation arises
if we compare the clump �SFR to the galaxy-averaged �SFR. Thisis shown in the right-hand panel of Fig. 7, and has a correlationcoefficient ρ = 0.79 with 6.6σ significance. The ratio of clump-to-average�SFR can be thought of as a measure of the ‘clumpiness’ ofthe galaxy.
Evolution in the properties of giant H II regions 697
Figure 7. Comparisons between the star formation surface density �SFR of star-forming clumps within each galaxy and the intrinsic Hα luminosity andgalaxy-averaged �SFR. The clump �SFR shown is the median for each galaxy, with error bars encompassing the full range of �SFR for all clumps within eachgalaxy. The solid line is the best fit to the data, and the dashed line illustrates the clump �SFR expected from theory, discussed in Section 4. We find that bothare correlated at the 5σ level, implying that we find more high �SFR clumps at high redshift because there are more high SFR and �SFR galaxies at this epoch.
We conclude that the properties of star-forming clumps in agalaxy are strongly dependent on the global �SFR of the galaxy.Galaxies with higher overall �SFR have higher clump surface den-sities and are correspondingly offset in the clump size–SFR relation.While this accounts for some of the differences seen in Fig. 6, it isalso clear that there are more bright clumps in the higher redshiftgalaxies. We quantify this below.
3.3 H II region luminosity functions
A quantitative measure of the clump brightness is to construct aLF of H II regions. In the local Universe, the H II LF is presented inKennicutt, Edgar & Hodge (1989) and Gonzalez Delgado & Perez(1997). They demonstrate that the LF can be fitted by a brokenpower law, or by a power law with an exponential break. In order tobe consistent with our definitions of clump sizes, we re-analyse thelocal data in order to construct our own LF. The results are shownin Fig. 8. The left-hand panel of the figure shows the cumulativenumber of regions per galaxy as a function of Hα luminosity. Thenormalization of each bin takes into account the different surfacebrightness limit of the galaxies, with error bars computed from thePoisson error in counting regions. The slope of the power-law part ofthe mass function is∼−0.75, so that although the LF appears steepin this representation, most of the total luminosity is contributed bythe brightest H II regions.Solid black points show the average of all SINGS galaxies. How-
ever, since we will be comparing the galaxies covering a range ofluminosities and redshifts, we have separated the galaxies from theSINGS sample into three total Hα luminosity bins. At a fixed lumi-nosity, galaxies with lower total emission have fewer regions, butthe shape of the LF is similar. In order to emphasize the similarityof the mass function, we normalize each of the curves by the total
SFR of the host galaxies, and show this in the right-hand panel. Thesimilarity of all the H II region LFs is now clear.There is a striking similarity between the LF of the z ∼ 1–1.5
sample and that of the highest SFR galaxies in the low-z SINGSsample. The excess of very bright regions (L ∼ 1041 erg s−1) isdown to one galaxy, Abell 773, which is the same compact galaxyfor which we found the clump surface brightnesses to be moretypical of the highest redshift galaxies. The low-luminosity slopeof the LF tends also to be flatter than that seen in the low-redshiftgalaxies, but it is hard to quantify this difference without directlycomparable surface brightness limits and is likely to be affectedby unresolved regions which are excluded. In any case, these faintregions contribute little to the total flux.In both panels, the H II region LF for the highest redshift galaxies
is strongly offset from the relation seen in the low-redshift SINGSsample and from the sample at z ∼ 1–1.5, but is similar to the low-redshiftULIRGs.Although the data do not probe the low-luminosityslope of the LF, these galaxies have much brighter regions than areseen at lower redshift. The right-hand panel emphasizes that this isnot because they contain many more regions overall.In order to compare our data to models of mass functions, we
must relate the measured Hα luminosities to model clump mass,M. As an estimate, we use the Hα-derived SFR and adopt SFR(M� yr−1) = 4.6 ± 2.6 × 10−8 M� (Lada, Lombardi & Alves2010). This empirical relation is based on local molecular cloudsand applies to the high-density gas where AK > 0.8mag. However,we note that this relation is consistent with the far-infrared-derivedSFR and CO-derived gas masses of star-forming clumps reported ina lensed z = 2.3 galaxy by Swinbank et al. (2011), but clearly morehigh-resolution CO observations of high-z galaxies are required toconfirm this. As a guide, we include this conversion on the upperaxis of Fig. 8.
Figure 8. Cumulative LFs of H II regions in the SINGS, z ∼ 1–1.5 and z ∼ 2 samples, shown as a mean per galaxy (left) and normalized by total galaxy Hα
luminosity (right). We plot the SINGS sample as a whole and subdivided into three luminosity bins. The shaded regions illustrate model predictions from theGMC mass functions of Hopkins, Quataert & Murray (2012) for Milky Way-like (grey) and high-z (blue) simulations. We find evolution in the H II region LFwith redshift, which seems to be driven by the gas fraction of the disc.
The shapes of the LFs can be approximated by a power law withan exponential cut-off at some high luminosity or mass. The dif-ference between the samples’ LFs is then best described by a pureluminosity evolution, so that the cut-off shifts to higher luminos-ity/mass at higher redshift.To demonstrate this, we include shaded regions representing a
Schechter function of the form
N (>M) = N0
(M
M0
)α
exp
(−M
M0
), (1)
where we adopt the median value of α = −0.75 from Hopkinset al. (2012). The normalization N0 is arbitrary, so we fit N0 tothe z = 0 data and then keep it fixed while allowing M0 to varyin order to find best-fitting values of in the different samples. Thebest-fitting values are M0 = 4.6+3.1
−2.0 × 107 M� at z = 0, M0 =8.0+11.0
−4.3 × 107 M� at z ∼ 1–1.5 and M0 = 1.5+2.2−1.0 × 109 M� at
z ∼ 2, where the errors are found with a bootstrap method. Weshade the best-fitting Schechter functions at z = 0 and z ∼ 2 in greyand blue, respectively, in Fig. 8. The normalization of the modelin the right-hand panel is obtained by summing the luminosities ofthe clumps. The result is in remarkably good agreement with ourobservations.Not only do the highest redshift galaxies have H II regions that
are higher surface brightness, but the characteristic luminosity ofthe regions is higher too. We suggest that the presence of high-luminosity regions may be a good operational definition of theclumpiness of a galaxy.
4 D ISCUSSION
In the previous section, we presented an analysis of star-formingregions in galaxies at z = 0, z ∼ 1–1.5 and z ∼ 2. We find that theluminosities of the regions in z = 1 galaxies are similar to those
of bright (L > 1040 erg s−1) galaxies at low redshift, but the sur-face brightnesses are systematically higher. At higher redshifts, theproperties of the galaxies change, with the galaxies having clumpsthat are both much higher surface brightness and shifted to highertotal luminosities. This accounts for the qualitative impression thatthe most distant galaxies are ‘clumpier’.We also noted that the increase in the surface brightness of H II
regions tracks the increase in the average SFR surface density,�SFR,of the galaxies. The observations are consistent with the changingproperties of the H II regions being driven by changes in the overall�SFR of the galaxies. We can link the increase in the observed�SFR to an increase in the gas surface density of these galaxies byassuming that the Kennicutt–Schmidt law holds at z ∼ 2 as well asat z = 0. In this case, we have an emerging picture that the changeswe see are likely driven by greater gas surface densities at higherredshift.The connection between the increasing surface density of clumps
and the greater peak brightness arises naturally from this picture(Hopkins 2012). The clump mass required for collapse on scale Rfrom a turbulent ISM is given by the Jean’s mass, MJ:
ρc = 3
4πR3MJ ≈ 9
8πR2Gσt(R)
2, (2)
whereσ t(R) is the line of sight turbulent velocity dispersion.Assum-ing a turbulent velocity power spectrumE(k), the velocity dispersionσ t(R) for wavenumber k = 1/R is
σ 2t = kE(k) ∝ Rp−1, (3)
where p ≈ 2 for supersonic turbulence appropriate to the ISM(Burgers 1974; Schmidt et al. 2009).To determine the normalization of the relation, we assume that the
clumps are located in a marginally unstable disc. We note that theavailable kinematic data for the z ∼ 2 sample and for MACS J1149
Evolution in the properties of giant H II regions 699
support this assumption, as do larger surveys (Genzel et al. 2011);nonetheless, clearly this is uncertain without dynamical data for theentire sample. However, if wemake the assumption that the galaxiesare rotating discs with Toomre parameter Q ≈ 1, we can relate theepicyclic frequency, κ of the disc to its scale height, h: κ ≈ σ t(h)/h,
Q = κσt(h)
πG�0≈ σt(h)2
πG�0h. (4)
Since the stability of the disc is a global phenomenon, we will asso-ciate �0 with the average surface density of the star-forming disc,�disc, and treat the quantities appearing in equation (4) as appropri-ate global disc averages. Since the disc is made up of both stars andgas, we must take an appropriate average of the surface densitiesin the two components. Following Rafikov (2001), and focusing onthe largest unstable fluctuations, the appropriate combination of gasand star surface densities (denoted �g and �∗) is
�disc = �g +(
2
1+ f 2σ
)�∗, (5)
where f σ = σ ∗/σ t is the ratio of the velocity dispersion of the stellarcomponent to that of the gas.Assuming Q ≈ 1, we can write
σ 2t (R) = (πG�disch)
(R
h
)p−1≈ πG�discR, (6)
where we have used equation (3) to relate σ t(h) to σ t(R). Combiningwith equation (2) gives a critical density for collapse of
ρc(R) = 9
8�disc
1
R. (7)
Assuming that the cloud contracts by a factor of≈2.5 as it collapses,the post-collapse surface density is
�cloud ≈ 10ρcR ≈ 10�disc. (8)
Thus, for the turbulent power spectrum p ≈ 2, the surface densityof collapsed clouds is independent of radius and proportional tothe surface density of the disc. The normalization of the relationfollows from the collapse factor and the requirement that the disc ismarginally stable. This model provides a good description of cloudsin the Milky Way (Larson’s laws) as discussed in Hopkins (2012),and predicts that the surface brightnesses of clouds should increaseas the gas surface density (and thus overall average SFR surfacedensity) increases. If we assume a constant Kennicutt–Schmidt lawof the form�gas ∝ �1.4
SFR (Kennicutt 1998b), we can compare equa-tion (2) to our data; we therefore overplot this line in Fig. 7 and findthat it is in good agreement with the observations.Moreover, themodel predicts that themostmassive clouds should
increase in size with the average gas surface density. This followsfrom the marginal stability condition (equation 4), since densitystructures on scales greater than h will tend to be stabilized by discrotation.This can be demonstrated formally by examining the dispersion
relation for a finite thickness disc (Begelman & Shlosman 2009).Hopkins (2012) shows that this leads to an exponential cut-off ofthe clump mass function above a mass
M0 ≈ 4π
3ρc(h)h
3 = 3π3G2
2
�3disc
κ4, (9)
where we have used equations (3) and (4) to express h as a functionof �disc and κ = vdisc/Rdisc (where vdisc is the disc circular velocityand Rdisc is half-mass radius of the disc). Expressing κ in units of100 km s−1 kpc−1 we obtain a normalization of
M0
M�= 8.6× 103
(�disc
10M� pc−2
)3 (κ
100 km s−1 kpc−1
)−4.(10)
We can check that this results in a reasonable value of M0 in theMilkyWay by using a gas surface density�gas ∼ 10M� pc−2 and agas fraction of 10 per cent with f σ = 2 (Korchagin et al. 2003) to ob-tain an effective �disc ∼ 35M� pc−2. With κ = 36.7 km s−1 kpc−1
(Feast &Whitelock 1997), this givesM0 ∼ 107 M�, in good agree-ment with the characteristic mass of the largest Galactic GMCs(Stark & Lee 2006).Equation (10) shows that the mass cut-off depends strongly on
the disc surface density – the higher the surface density, the moremassive the clumps that are able to form. This trend can, however,be opposed by the stabilizing effect of angular rotational speed. Fora fixed disc radius, a higher circular velocity tends to reduce themass of the largest clumps.For low-redshift galaxies, simple theoretical models suggest that
Rdisc ∝ vdisc since halo spin is weakly dependent on the halo mass(Mo, Mao & White 1998), and thus we should expect the depen-dence on the disc surface density to be the dominant trend control-ling the cut-off clump mass. This is confirmed by analysis of theobserved properties of galaxies. For example, Dutton et al. (2011)find
Rdisc
kpc≈ 2.5
(vdisc
100 km s−1
)1.2
(11)
in the local universe. Combining this with the observed dependenceof the disc rotation velocity on galaxy mass
M∗1010 M�
= 0.25
(vdisc
100 km s−1
)4.5
, (12)
we obtain
κ
100 km s−1 kpc−1≈ 0.38
(M∗
1010 M�
)−0.04, (13)
which shows that κ is very weakly dependent on the galaxy mass,and the variation in the clump mass functions of local galaxies isdriven by the disc surface density.We also note that in a disc of constant circular velocity, κ scales
with radial distance r as κ ∝ r−1, while the gas surface densityprofiles are shallow, with �gas ∝ r−4/3 (Fu et al. 2010). Thus fromequation (10) there is no dependence of M0 on r; while the surfacedensity is higher towards the centre of the galaxy, this is balancedby the higher rotational frequency. This explains the observationsthat clump properties appear to be driven by the global properties oftheir host galaxies rather than by local conditions, and this allowsus to use disc-averaged values of κ and �.We have no measurements of the gas contents of our samples,
but dynamical information available for the z ∼ 2 sample permitsus to predict the cut-off mass in these galaxies from our model if weestimate �disc from the dynamical mass. Using the measurementsreported in Jones et al. (2010, see their table 2), we compute a cut-offmass ranging from 3.3× 106 to 3.1× 109 M� for the z ∼ 2 sample.The median value is 5 × 107 M�, approximately 5 × higher thanthe Milky Way value. We therefore expect that the z ∼ 2 sampleshould contain clumps of higher mass and luminosity, as observed.However, the uncertainty in the cut-off mass for the z ∼ 2 sampleis very large due to uncertainties in �disc and κ , which preventsus from making a precise comparison of the cut-off mass in thedifferent samples.To understand how the clumpiness of galaxies evolves, we must
therefore use simulations to estimate the evolution of their scal-ing relations. Dutton et al. (2011) present a simple analytic modelthat seems to describe the observational data well (Trujillo et al.2006; Forster Schreiber et al. 2009; Williams et al. 2010). We use
Figure 9. The evolution of cut-off mass M0 and clump surface density �clump in comparison with model predictions (equation 10). The model is stronglydependent on the assumed evolution of gas fraction with redshift; we show tracks for f gas ∝ (1+ z)2 ±0.5 and the thick arrows show the effect of increasing thegas fraction. We also show a track for f σ = 1 – i.e. assuming that the gas and stars have the same velocity dispersion. This makes the disc unstable on largerscales and would lead to higher mass clumps at low-z than are observed. The impact of this is reduced at higher z where gas dominates the disc dynamics. Asf σ increases, the points move in the direction of the arrow in the lower right-hand corner. The model provides a good fit to the data, demonstrating that larger,higher surface brightness clumps at high-z are a natural consequence of increasing gas fractions, which explains the observed morphologies of high-z galaxies.
their scaling relations for mass, size and rotational frequency withredshift in combination with equations (8) and (10) to predict howthe cut-off mass and clump surface brightness should evolve withredshift. Fig. 9 illustrates this evolution for a gas fraction evolutionof f gas ∝ (1 + z)2 ±0.5 (Geach et al. 2011). The arrows show howaltering the assumed gas fraction changes the model. This suggeststhat the changing clump properties are a natural consequence ofincreasing gas fractions dominating high-z galaxy dynamics. Thehigh gas fractions probably arise from high gas infall rates at highredshift (Bournaud & Elmegreen 2009; Krumholz & Dekel 2010;Bournaud et al. 2011); however, our observations do not directlyrule in or out cold flows. Our results merely require high gas frac-tions, and cold flows are a method of maintaining the gas supply.Crucially, we note that this effect is tempered by the more compactnature of galaxies, which leads to higher epicyclic frequencies thatlimit the collapse on larger scales. The need to include the κ termis apparent from our H II region LFs: without it, a factor of 10 in-crease in disc surface density would correspond to an increase in
clump luminosity of 1000×, and we do not observe such a largeincrease.To summarize, we find that our simple theoretical model is in
good agreementwith the observations and suggests that the evolving‘clumpiness’ of galaxies is a manifestation of the different cut-offmass of the H II region LF, which is driven by evolution in the gasfraction with redshift.
5 C O N C L U S I O N S
We have used HST/WFC3 to obtain narrow-band Hα imaging ofeight gravitationally lensed galaxies at z ∼ 1–1.5. Themagnificationprovided by the lensing enables us to reach spatial resolutions inthe source plane of 68–615 pc. In addition, to provide compar-isons we have re-analysed the lensed z ∼ 2 sample observed withKeck/OSIRIS by Jones et al. (2010), the Rodrıguez-Zaurın et al.(2011) sample of z < 0.13 (U)LIRGs observed with VLT/VIMOS
Evolution in the properties of giant H II regions 701
and the Hα narrow-band imaging of the z = 0 SINGS survey(Kennicutt et al. 2003).The high-z samples have ‘clumpy’ morphologies, dominated by
a few large regions of high Hα luminosity, which we use as aproxy for the SFR. We have extracted star-forming clumps from thegalaxies in each sample and examined their properties. The clumpsfollow similar SFR–size scaling relations in all samples, but thenormalization of the relation exhibits systematic offsets to highersurface brightness at higher redshifts. The normalization appears tobe approximately constant within a given galaxy, implying that thisrelation is driven by global galaxy properties.On comparison with the properties of the host galaxies, we find
that all samples follow approximately the same scaling relationsbetween the clump surface brightness and both the host galaxy’stotal Hα luminosity, LHα , and its average surface density of star for-mation,�SFR, and that they evolve along this relation in decreasingLHα and �SFR with decreasing redshift.We have measured the LF of clumps in the samples, and shown
that the z ∼ 1–1.5 sample is similar to the higher LHα members ofthe SINGS sample. When normalized by the host galaxies’ totalSFR, the SINGS and z ∼ 1–1.5 samples can be fit by the sameSchechter function, while the (U)LIRGs and z ∼ 2 samples areoffset horizontally. This shift can be explained by an increase in thecut-off mass of the H II region LFs of the (U)LIRGs and z ∼ 2 discs.We present a simple theoretical model which shows that the
evolution in luminosity and surface brightness are connected, andare driven by the competing effects of disc surface density�disc andthe epicyclic frequency κ . Galaxies at high redshift tend to havehigher�disc, which increases the maximummass of clumps that areable to form; however, this is tempered by the more compact natureof high-z galaxies, implying higher κ , which impedes collapse onthe largest scales.We have shown that this model is consistent with the evolution
in clump properties seen in our data. We therefore conclude that theclumps observed in high-z galaxies are star-forming regions anal-ogous to those found locally but with higher masses and surfacebrightnesses. As H II regions in the distant Universe are larger andbrighter, they give rise to the ‘clumpy’ appearance. The increasein clump luminosity is driven primarily by increasing gas fractionsat high-z. This clearly motivates further study with Atacama LargeMillimeter/submillimeter Array (ALMA) to better quantify the evo-lution of gas properties in high-z galaxies.
AC K N OW L E D G M E N T S
The authors would like to thank Karl Glazebrook, EmilyWisnioski,Lisa Kewley and Norm Murray for useful discussions and AndrewNewman for providing an updated strong lensing model of thecluster Abell 611. RCL acknowledges a studentship from STFC,RGB and IS are supported by STFC and IS further acknowledgesa Leverhulme Senior Fellowship. AMS acknowledges an STFCAdvanced Fellowship, and JR is supported by the Marie CurieCareer Integration Grant 294074. HE gratefully acknowledges fi-nancial support from STScI grants GO-09722, GO-10491, GO-10875 and GO-12166. This work is based on observations with theNASA/ESA Hubble Space Telescope obtained at the Space Tele-scope Science Institute, which is operated by the Association ofUniversities for Research in Astronomy, Inc., under NASA contractNAS5-26555. Support for Program number 12197 and Programnumber 11678 was provided by NASA through a grant from theSpace Telescope Science Institute, which is operated by the Associ-
ation of Universities for Research in Astronomy, Inc., under NASAcontract NAS5-26555.
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This paper has been typeset from a TEX/LATEX file prepared by the author.
